LCM of 25 and 36 is 900. The smallest number among all common multiples of 25 and 36 is the LCM of 25 and 36. (25, 50, 75, 100, etc.) and (36, 72, 108, 144, 180, 216, etc.) are the first few multiples of 25 and 36, respectively. Various approaches, such as prime factorization, division, and listing the multiples, can be used to quickly find the LCM. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 25 and 36?
The answer to this question is 900. The LCM of 25 and 36 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 25 and 36, is the smallest positive integer 900 which is divisible by both 25 and 36 with no remainder.
How to Find LCM of 25 and 36?
LCM of 25 and 36 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 25 and 36 Using Prime Factorisation Method
The prime factorisation of 25 and 36, respectively, is given by:
25 = (5 × 5) = 52 and
36 = (2 × 2 × 3 × 3) = 22 × 32
LCM (25, 36) = 72
LCM of 25 and 36 Using Division Method
We’ll divide the numbers (25, 36) by their prime factors to get the LCM of 25 and 36 using the division method (preferably common). The LCM of 25 and 36 is calculated by multiplying these divisors.
| 2 | 25 | 36 |
| 2 | 25 | 18 |
| 3 | 25 | 9 |
| 3 | 25 | 3 |
| 5 | 25 | 1 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (25, 36) = 900
LCM of 25 and 36 Using Listing the Multiples
To calculate the LCM of 25 and 36 by listing out the common multiples, list the multiples as shown below
| Multiples of 25 | Multiples of 36 |
| 25 | 36 |
| 50 | 72 |
| 75 | 108 |
| ….. | …… |
| 900 | 900 |
The smallest common multiple of 25 and 36 is 900.
Therefore LCM (25, 36) = 900
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LCM of 25 and 36 Solved Example
Question: The GCD and LCM of two numbers, respectively, are 1 and 900. Find the other number if one of the numbers is 36.
Solution:
Let the other number be a.
∵ GCD × LCM = 36 × a
⇒ a = (GCD × LCM)/36
⇒ a = (1 × 900)/36
⇒ a = 25
Therefore, the other number is 25.
Frequently Asked Questions on LCM of 25 and 36
What is the LCM of 25 and 36?
List the methods used to find the LCM of 25 and 36.
If the LCM of 36 and 25 is 900, Find its GCF.
Since the LCM of 36 and 25 = 900
⇒ 900 × GCF(36, 25) = 900
Therefore, the GCF = 900/900 = 1.
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